The Rock and Roll Hall of Fame audience had to wait a long time for Nirvana to hit the Barclays Center stage on Thursday night.

More than four hours into a show that veered between galvanizing and grueling, the band's surviving members, Dave Grohl and Krist Novoselic, its special guests, family, extended-family and new family members got it just about perfect, from the speeches to the four-song performance, which saw the group fronted by carefully chosen female singers who ran a fitting and fascinating spectrum across the band's history and its influence.

It added up to a tribute to Kurt Cobain and Nirvana's history and legacy that carried all of the dignity and respectful reverence that its surviving members have shown over the past 20 years.

And whatever wasn't perfect was, in its way, perfectly appropriate.

The five-years-and-change arc of the band's career dovetailed with the Rock Hall's schedule to make this evening the cap on a crescendoed series of 20th-anniversary landmarks -- In Utero, Unplugged, the final gig and Cobain's April 5 death -- since September. Thus, a certain degree of Nirvana fatigue is to be expected, which makes the evening's achievement all the more remarkable.

The choice of the singers who fronted the band was nothing short of masterful: One performer who influenced the core band members as teens, and even produced the only album by late-era guitarist Pat Smear's first band, the Germs (Joan Jett); another who was both an influence and a key mentor early in the band's career (Sonic Youth's Kim Gordon); another who discovered Nirvana at the age of 9 and has gone on to a highly individual career -- and is herself a shredding guitarist (St. Vincent's Annie Clark); and finally, a highly individual teenaged singer (Lorde) who wasn't even born when Cobain died, and who looks to be doing a good job so far of facing down the star machine that caused him so much pain.

Michael Stipe was arguably the only person to induct the band: an influence, a fan, a friend and someone who saw the darkness spreading over Cobain and reached out to him in the final months of his life. According to a Hall source, there was talk of the R.E.M. frontman singing "All Apologies," but the plan was scrapped to make way for the girls (specifically, Lorde).

Stipe took the stage after a five-minute-long historical video introducing the band ("I'm always in pain, and that adds to the anger in our music," is one of several Cobain quotes in the video).

"It is the highest calling for an artist as well as the greatest possible privilege to capture a moment, to find the zeitgeist, to expose our struggles, our aspirations, our desires, to embrace and define their time," Stipe said. "Nirvana captured lightning in a bottle. The potency and the power of their defining moment has become, for us, indelible."

"Solo artists almost have it easier than bands; bands are not easy. You find yourself in a group of people. You rub each other the wrong way in exactly the right way, and you have chemistry, lighting in a bottle, and a collective voice to help pinpoint a moment. To understand what it is that we're going through. Nirvana tapped into a voice that was yearning to be heard.

"They spoke truth and a lot of people listened. They picked up the mantle of that particular battle. Hey, we're singular loud melodic and deeply original, and that voice … that voice. Kurt, we miss you. I miss you."

Brief speeches from Grohl -- who classily thanked each of the Nirvana drummers who preceded him, particularly Chad Channing -- Novoselic, Kurt's mom, Wendy Cobain, and Courtney Love followed. Courtney kept hers short and focused on thanks, including "Frances, our daughter, who can't be here because she's ill." The appearance marked a poignant detente between Grohl and Love, who've had a cantankerous relationship for years.

The band took the stage with Jett, and wasted no time getting into a flawless rendition of "Smells Like Teen Spirit" (days ago, we predicted both the song choice for Jett, and that it would be awesome). Jett positively nailed the song, bringing the perfect amount of both melody and throat-shredding gravel to it, soaring on the choruses, and bringing a Gibson roar with her guitar playing that perfectly complimented Smear's phased, subtler sound. It's hard to describe the emotion of seeing the band play the song again -- Novoselic twisting, Grohl's hair flying -- after all these years; the cameras cut to Wendy Cobain at her table, smiling and weeping at the same time. Jett looked enormously relieved when she finished -- but she also knew she'd nailed it.

Kim Gordon, clad in a striped, Riot Grrrl-esque dress, was up next for "Aneurysm," an unexpected but perfect choice for her singing style. She bounced all over the stage, falling at one point -- probably by accident, but she went with it, yelling into the mic from the floor as if it were part of the plan. She exited the stage laughing, thanking "Frances, Kurt, Courtney, Krist, Dave and everybody f-----' else." Very punk rock.

Annie Clark brought her own badass-ness to "Lithium" with some overdriven guitar and a vocal performance that wasn't as shredding as Jett's -- who's is? -- but with plenty of power and her distinctive quaver toward the end. Like Jett, she had a look of palpable relief on her face at the end.

Finally, Lorde, clad in hot pink suit and black halter top, came out for "All Apologies." Krist switched to accordion, Gordon played bass and Jett and Clark joined in on guitars. Like Clark, Lorde brought a deep, un-Cobain-like but still fitting vocal performance to the song, doing her trademark animal-like arm gestures, dropping down even lower for the "all we know is all we are" repetition at the end. The camera cut to a teary-eyed Stipe and Love standing side-by-side at their table.

Images of Cobain and the band had been projected behind the musicians for the entire performance, and the last was a shot of Kurt Cobain (photographed by Jeff Kravitz) at the mic during the "In Utero" tour, with the wings from the mannequin feature on the album cover sprouting out from his shoulders angelically. That image remained on the screen as the crowd filed out.

Earlier in the evening in the press room, Clark talked about the influence Nirvana had on her. "Nevermind came out when I was 9 and it changed my life," she said. "It's the reason I'm playing music. I would be lying if I said [tonight] weren't a little melancholy."

Asked about the decision to have women front the band, she said, "Those guys were feminists in the early '90s, when it wasn't hip to be, and they were rad and forward-thinking. If you're going to play these songs again, do it from a little bit of a different angle." She added that "the most surreal moment [of the past few days] was hearing Dave, Krist and Pat f---ing playing."

Stipe was asked about the first time he met Kurt Cobain. "He was late," said the singer. "It was in Krist's basement. He and Courtney had moved into the house next door to my former guitar player Peter Buck; they lived side-by-side. ... The first time I looked into his eyes, I thought, 'I get it. He really is all that.' He was a really special person [And] he had really blue eyes."

Following the ceremony, the Nirvana super group reunited at Brooklyn's St. Vitus bar where, as of 3 a.m., they were still playing. More details to come.